Course Description
Measurable spaces and measures, Lebesgue-Stieljes measure, independence, almost sure and in probability convergence, integration in probability spaces, product measures, absolute continuity of measures, weak law of large numbers, strong law of large numbers, weak convergence.
Athena Title
PROBABILITY I
Prerequisite
STAT 6820 or permission of department
Semester Course Offered
Offered fall
Grading System
A - F (Traditional)
Course Objectives
This course is a first course in theoretical probability. The students will learn measure theory as it is applicable to probability. The fundamental theorems of probability will be covered. Complete proofs of results discussed in class will normally be presented. After completing this course, students will have an understanding of the theoretical underpinnings of probability, a knowledge of the key results in the area and will be able to prove results in this subject. The course provides essential background for advanced study of statistical inference and for conducting statistical research.
Topical Outline
Sigma fields, measurable functions, measures, Lebesgue integral, independence, almost sure convergence, product measures, distribution functions, weak law of large numbers, strong law of large numbers, three-series theorem, weak convergence, characteristic functions, central limit theorem, conditional expectation, and martingales.
Syllabus